
\(b \rightarrow c \ell \nu \) :
the NP effect on this process is significant since the \(|V_{cb}|\)  measurement is probed from the distribution data of the process.
According to the previous analysis in Ref. [1]}, non-zero NP contributions of \(C_{V_2, T}^{c\ell } (m_b)\)  are possible at 1–\(2\sigma \)  significance as shown in the figure.
The scalar scenarios for the electron mode are very restricted from the requirement of \(\mathcal {B}(B_c \rightarrow e\nu ) < 30\%\)  while those for muon mode are less constrained.
The present LHC bounds generally look milder than the flavor ones.
However, we can see that the results for \(C_T^{ce}\) , \(C_T^{c\mu }\) , and \(C_{S_{1,2}}^{c\mu }\)  are well competitive.


\(b \rightarrow c \tau \nu \) :
the current \(R_{D^{(*)}}\)  excesses are explained by the \(V_1\) , \(V_2\) , and \(T\)  scenarios as shown in the red bars,
and the LHC bounds are very comparable to these flavor-favored regions.
Our constraints in the EFT limit are weaker than that of Ref. [2]} but consistent with Ref. [3]}.
Then, it is quite significant whether the EFT limit is applicable or not to the corresponding LQ model.
In particular, we found that the \(V_2\)  and \(T\)  solutions to the excesses are almost excluded by the LHC bounds in the EFT limits
whereas these scenarios are still allowed in the LQ models with \(M_\text{LQ} = 2\,\text{TeV}\) .
For the scalar scenarios, see Sec. .


\(b \rightarrow u \ell \nu \) :
At present, the flavor bound is available only from \(B \rightarrow \ell \nu \) .
For both the electron and muon modes, the scalar scenarios with \(|C_{S_i}^{u\ell }| \lesssim \mathcal {O}(0.01)\)  are allowed from the flavor bound, which is much severer than the LHC bound.
Regarding the vector scenarios, on the other hand, the flavor and LHC bounds are comparable for the muon mode.
Note that the other NP scenarios, \(C_{V_{1,2},T}^{ue}\)  and \(C_{T}^{u\mu }\) , are more constrained from our LHC study than the leptonic processes.
See also Ref. [4]}.
A comprehensive fit analysis for \(B \rightarrow (\pi ,\rho ,a_1)\ell \bar{\nu }\)  in the presence of the NP effects for the flavor bound would be our future work.


\(b \rightarrow u \tau \nu \) :
the LHC bounds are loose, naively given as \(|C_{X}^{u\tau } (m_b)| \lesssim \mathcal {O}(1)\) .
Nevertheless, the LHC bound is already significant for the tensor scenario, which excludes a part of the allowed regions from the flavor bound.
We can also confirm importance of the non-EFT case as well as the other currents.

